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What's the Difference? Formative and Summative Mathematics Assessment

By Susan Carter

Assessment in mathematics no longer divides those “good at Math” from those “not good at Math.” Today, math instruction and assessment provide opportunities for students to make deeper connections, perform worthwhile tasks, and apply math in their daily lives.

Some of us may have grown up dreading traditional Math Tests. If we got mostly right answers, we felt like we were good at math, and if we got mostly wrong answers, well maybe mathematics wasn’t for us. We may have memories of finishing a unit in math and taking a timed computation test. Afterwards, we felt relieved to be finished and fairly confident that the topic would not come up again. Good news! Times have changed.

Assessment is an ongoing and integral part of math instruction that enhances both teaching and learning math. Teachers give students opportunities to show what they know through varied and frequent assessments.Giving various types of mathematics assessments gives teachers a clearer picture of how their students are progressing. It also allows the teacher to adjust for the needs of different types of learners.

Assessment for the purpose of “forming” or guiding instruction is called formative assessment. Assessment for the purpose of judging a student’s mastery of concepts is called summative assessment. Both are essential components of effective assessment and best practices in teaching.

Formative Assessment

Teachers assess their students in a variety of ways for a variety of reasons. In today’s math class, assessment is a key component of daily practice. Not all assessment is in search of a letter or number grade for the sole purpose of reporting student achievement (or lack there of). Teachers use formative assessment to determine what their students know already and what they need to know. Students can also use assessment to become aware of their own progress and areas of strength. They have access to rubrics and scoring guides that help to shape learning. Teachers use information about their students’ prior knowledge to help plan relevant lessons. Information gained from assessment is used to monitor student progress, inform parents of student achievement, and plan instruction.

Teachers can assess students accurately if they can understand how a student arrived at their solution. Students should have opportunities to express their mathematical ideas both orally and in writing. When a student is asked for a written explanation, it often helps the student clarify his or her thinking. A written explanation requires effort and editing on the part of the student. It is a window into a student’s thinking and gives the teacher a more exact understanding of their mathematical progress. Types of formative assessments include conversation, observation, journal writing, self-assessment and daily work.

Summative Assessment

Summative assessment is used to determine what students know about mathematics content and problem solving. Tests and quizzes tell the teacher if students can apply procedures and perform computations accurately. Standardized tests provide data about student performance in relation to other students. A standardized test is administered under the same conditions and scored in the same manner for all students. There is usually only one right answer. In order to get an accurate score, the directions and time limit must be the same for all students. Standardized tests allow comparisons to be made among students taking the test. These scores can also help schools and districts see patterns and make changes to improve student achievement over time.

Constructed response or performance tasks can help show students capacity to apply information in new situations. These types of assessments are an important component in determining what students know and what they need to learn in mathematics. It is important for teachers to understand how to analyze and apply results of standardized test scores in a classroom so that they can make the most of instructional time.